Audrius Meškauskas, Liam J. McNulty and David Moore*

School of Biological Sciences, Stopford Building, The University of Manchester, Oxford Road, Manchester M13 9PT, United Kingdom (*Corresponding author)

Abstract: Filamentous hyphal growth is inherently suited to kinetic analysis, and in many respects the fungal mycelium can be viewed as a very mechanical biological system, which lends itself to mathematical modelling. The mathematics of hyphal tip extension growth are well established. However, even though a hyphal growth equation can be written with confidence, and we have a good understanding of the effects of tropisms on growth, it is not easy to form a mental picture of the behaviour of large populations of hyphal tips. What is required, and what we believe we have produced, is a mathematical model that is sufficiently sophisticated to produce a realistic visualisation of fungal hyphal growth. This provides us with a cyberfungus that can be used for experimentation on the theoretical rules that might govern hyphal patterning, hyphal interactions, and tissue formation and organ development by actually visualising the virtual hyphal growth patterns that result from different regulatory scenarios. From a series of model experiments the most significant observation is that complex fungal fruit body shapes can be simulated by applying the same regulatory functions to all of the growth points active in a structure at any specific time. No global control of fruit body geometry is necessary. No localised regulation is necessary. The shape of the fruit body emerges from the concerted response of the entire population of hyphal tips, in the same way, to the same signals.

Original reference:

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Simulating colonial growth of fungi with the Neighbour-Sensing model of hyphal growth

Audrius Meškauskas, Mark D. Fricker¹ and David Moore*

School of Biological Sciences, Stopford Building, The University of Manchester, Oxford Road, Manchester M13 9PT, UK. and ¹Department of Plant Sciences, University of Oxford, South Parks Road, Oxford OX1 3RB, UK. (*Corresponding author)

The Neighbour-Sensing model brings together the basic essentials of hyphal growth kinetics into a vector-based mathematical model in which the growth vector of each virtual hyphal tip is calculated by reference to the surrounding virtual mycelium. The model predicts the growth pattern of many hyphae into three spatial dimensions and has been used to simulate complex fungal fruit body shapes. In this paper we show how the Neighbour-Sensing model can simulate growth in semi-solid substrata like agar or soil, enabling realistic simulation of mycelial colonies of filamentous fungi grown in ‘Petri-dish style’ experimental conditions. Newly implemented capabilities in the model include: a measurement and logging system within the program that maintains basic statistics about the mycelium it is simulating, this facilitates kinetic experimentation; inclusion of ‘substrates’ in the data space causing positive or negative tropisms for the growing mycelium; a horizontal plane tropism that provides a way of simulating colonies growing in or on a substratum like agar or soil by imposing a horizontal geometrical constraint on the data space the cyberhyphal tips can explore; three categories of hypha - standard hyphae are those that start the simulation, leading hyphae can emerge from the colony peripheral growth zone to take on a leading role, and secondary hyphae are branches that can arise late, far behind the peripheral growth zone, when mature hyphal segments resume branching to in-fill the older parts of the colony. We show how the model can be used to investigate hyphal growth kinetics in silico in experimental scenarios that would be difficult or impossible in vivo. We also show that the Neighbour-Sensing model can generate sufficiently realistic cord-like structures to encourage the belief that this model is now sufficiently advanced for parameters to be defined that simulate specific in silico cyberfungi. The potential utility of these cyberspecies is that they provide a means to model the morphogenetic effects of a variety of factors, from environmental and nutritional features to mutations, in experimentally realistic situations, offering a valuable addition to the experimental toolkit of all those interested in fungal growth and morphology.

Original reference:

Submitted to Mycological Research 16 May 2004, accepted 29 July 2004

You can DOWNLOAD a complete PDF file of a preprint of this manuscript, but beware - it's over 1.6 Mb.

Branching in fungal hyphae and fungal tissues: growing mycelia in a desktop computer

David Moore, Liam J. McNulty and Audrius Meškauskas*

School of Biological Sciences, Stopford Building, The University of Manchester, Oxford Road, Manchester M13 9PT, United Kingdom, and *Gediminas Technical University, Saulėtekio al. 11, LT-2040 Vilnius, Lithuania

Abstract: In mycelial fungi the formation of hyphal branches is the only way in which the number of growing points can be increased. Cross walls always form at right angles to the long axis of a hypha, and nuclear division is not necessarily linked to cell division. Consequently, no matter how many nuclear divisions occur and no matter how many cross walls are formed there will be no increase in the number of hyphal tips unless a branch arises. Evidently, for the fungi, hyphal branch formation is the equivalent of cell division in animals, plants and protists. The position of origin of a branch, and its direction and rate of growth are the crucial formative events in the development of fungal tissues and organs. Kinetic analyses have shown that fungal filamentous growth can be interpreted on the basis of a regular cell cycle, and encourage the view that a mathematical description of fungal growth might be generalised into predictive simulations of tissue formation. An important point to emphasise is that all kinetic analyses published to date deal exclusively with physical influences on growth and branching kinetics (like temperature, nutrients, etc.). In this chapter we extrapolate from the kinetics so derived to deduce how the biological control events might affect the growth vector of the hyphal apex to produce the patterns of growth and branching that characterise fungal tissues and organs. This chapter presents: (i) a review of the published mathematical models that attempt to describe fungal growth and branching; (ii) a review of the cell biology of fungal growth and branching, particularly as it relates to the construction of fungal tissues; and (iii) a section in which simulated growth patterns are developed as interactive three-dimensional computer visualisations in what we call the Neighbour-Sensing model of hyphal growth. Experiments with this computer model demonstrate that geometrical form of the mycelium emerges as a consequence of the operation of specific locally-effective hyphal tip interactions. It is not necessary to impose complex spatial controls over development of the mycelium to achieve particular morphologies.

Original reference:

You can DOWNLOAD a complete PDF file replica of this chapter, but for copyright reasons this is a non-printing version (though there's nothing to stop you saving it to disk to read at leisure).

An experimental tool to study fungal networks: the Neighbour-Sensing mathematical model of hyphal growth

Audrius Meškauskas, Liam J. McNulty and David Moore

School of Biological Sciences, Stopford Building, The University of Manchester, Oxford Road, Manchester M13 9PT, United Kingdom (e-mail: david.moore@man.ac.uk)

We describe here a simple mathematical model and computer program that provides a life-like tool that enables experimentation on the impact of tropisms by actually visualising the virtual hyphal growth patterns. We call it the Neighbour-Sensing mathematical model of hyphal growth because the growth vector of each virtual hyphal tip depends upon values derived from its surrounding virtual mycelium. Effectively, the virtual hyphal tip is sensing the neighbouring mycelium. The program produces very realistic simulations and promises to provide a meaningful experimental tool to study hyphal networks.

Original reference:

You can DOWNLOAD a complete PDF file of this chapter, but for copyright reasons this is a non-printing version (though there's nothing to stop you saving it to disk to read at leisure).

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